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    "### 1. **What is the Central Limit Theorem?**\n",
    "**Answer:**\n",
    "The Central Limit Theorem states that, regardless of the population distribution, the sampling distribution of the sample mean will be approximately normally distributed if the sample size is large enough. This is crucial because it allows us to make inferences about the population mean based on sample data.\n",
    "\n",
    "### 2. **Explain the difference between Type I and Type II errors.**\n",
    "**Answer:**\n",
    "- **Type I Error (False Positive):** This occurs when we reject a true null hypothesis. It means we detect an effect that doesn't actually exist. The probability of Type I error is denoted by α (alpha), and it's the significance level we choose.\n",
    "- **Type II Error (False Negative):** This occurs when we fail to reject a false null hypothesis. It means we miss a real effect. The probability of Type II error is denoted by β (beta), and it depends on factors like sample size, effect size, and significance level.\n",
    "\n",
    "### 3. **What is p-value and how do you interpret it?**\n",
    "**Answer:**\n",
    "The p-value is the probability of observing a test statistic as extreme as, or more extreme than, the one calculated from your data, assuming the null hypothesis is true. It helps us decide whether to reject or fail to reject the null hypothesis.  \n",
    "**Interpretation:** If the p-value is less than or equal to the chosen significance level (α), we reject the null hypothesis. If the p-value is greater than α, we fail to reject the null hypothesis. A smaller p-value indicates stronger evidence against the null hypothesis.\n",
    "\n",
    "### 4. **Explain the difference between correlation and causation.**\n",
    "\n",
    "**Answer:**\n",
    "- **Correlation:** Correlation measures the statistical relationship between two or more variables. It tells us how variables change together, but it does not imply causation. For example, ice cream sales and the number of drownings are correlated, but one does not cause the other.\n",
    "- **Causation:** Causation implies a cause-and-effect relationship between variables. It means changes in one variable directly cause changes in another. Establishing causation often requires controlled experiments.\n",
    "\n",
    "### 5. **What is a confidence interval?**\n",
    "**Answer:**\n",
    "A confidence interval is a range of values within which we believe the true population parameter lies with a certain level of confidence. For example, if we say we are 95% confident that the true population mean falls within a certain range, it means that in 95 out of 100 samples, the true population mean will fall within that range.\n",
    "\n",
    "### 6. **Explain ANOVA and its use cases.**\n",
    "**Answer:**\n",
    "ANOVA, or Analysis of Variance, is a statistical technique used to compare means between two or more groups. It's used when you want to determine if there are significant differences among the group means.\n",
    "\n",
    "**Use Cases:**\n",
    "- Comparing means across multiple groups (e.g., teaching methods).\n",
    "- Experimental designs with multiple independent variables or conditions.\n",
    "- Quality control in manufacturing.\n",
    "\n",
    "### 7. **What is a p-value threshold and why is it important?**\n",
    "**Answer:**\n",
    "A p-value threshold is the level of significance chosen to determine whether to reject or fail to reject the null hypothesis. Common thresholds are 0.05 (5%) and 0.01 (1%).\n",
    "\n",
    "It's important because it sets the criteria for how strong the evidence against the null hypothesis needs to be before we reject it. Choosing an appropriate threshold balances the risk of Type I and Type II errors.\n",
    "\n",
    "### 8. **Explain the concept of power in hypothesis testing.**\n",
    "**Answer:**\n",
    "Power is the probability of correctly rejecting a false null hypothesis. It measures the ability of a test to detect a true effect. A high power indicates that the test is good at detecting real differences or relationships.\n",
    "\n",
    "### 9. **Explain the concept of A/B testing.**\n",
    "**Answer:**\n",
    "A/B testing (or split testing) is a method used to compare two versions of a webpage or app against each other to determine which one performs better. It involves showing two versions (A and B) to different users and measuring their response to determine which version is more effective.\n",
    "\n",
    "### 10. **Explain the concept of bootstrapping in resampling methods. How does it help in estimating the uncertainty of a statistic?**\n",
    "**Answer:**\n",
    "Bootstrapping is a resampling technique where multiple samples (with replacement) are drawn from the original dataset to estimate a statistic. By creating multiple \"pseudo-populations,\" it provides an empirical way to estimate the sampling distribution of a statistic, allowing us to compute confidence intervals and make inferences about the population parameter.\n",
    "\n",
    "### 11. **What is the purpose of a Q-Q plot (Quantile-Quantile plot) in statistics? How do you interpret it?**\n",
    "**Answer:**\n",
    "A Q-Q plot is used to visually assess if a dataset follows a certain distribution (e.g., normal distribution). It compares the quantiles of the data with the quantiles of a theoretical distribution. If the points in the plot closely follow a straight line, it indicates that the data is approximately normally distributed.\n",
    "\n",
    "### 12. **Explain the concept of stratified sampling. When and why would you use it?**\n",
    "**Answer:**\n",
    "Stratified sampling involves dividing the population into homogeneous subgroups (strata) and then randomly selecting samples from each stratum. It ensures that each subgroup is well-represented in the sample, which can improve the accuracy of estimates for specific groups within the population. It's used when there are known differences within the population that need to be captured in the sample.\n",
    "\n",
    "### 13. **Explain the concept of non-parametric statistics. Provide examples of non-parametric tests.**\n",
    "**Answer:**\n",
    "Non-parametric statistics do not make assumptions about the underlying distribution of the data. They are used when the data may not meet the assumptions of parametric tests.\n",
    "\n",
    "**Examples of Non-parametric Tests:**\n",
    "- Mann-Whitney U Test (Wilcoxon Rank-Sum Test)\n",
    "- Kruskal-Wallis Test\n",
    "- Spearman's Rank Correlation"
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